Cambridge A Level Physics 9702 — 2016 Feb/March Paper 3 · Variant 3

1 In this experiment you will investigate the behaviour of a sphere rolling across a sloping board. (a) Pass the thread through the hole in the board and clip it in place with the spring clip. Set up the apparatus as shown in Fig. 1.1, with the board at an angle of approximately 45° to the bench. The length of the thread between the spring clip and the sphere should be approximately 20 cm. spring clip thread sphere boss wooden strip clamp G-clamp stand board § 45° bench Fig. 1.1 (not to scale) (b) (i) Measure and record the angle θ between the board and the bench, as shown in Fig. 1.2. spring clip sphere board e bench Fig. 1.2 (not to scale) θ = ..................................................[1] (ii) Push the sphere to one side. Release the sphere so that it oscillates from side to side. (iii) Take measurements to find the period T of the oscillations. Record T. T = ............................................... s [2] (c) Change θ by moving the boss and clamp and repeat (b) until you have six sets of values for θ and T. Do not change the length of the thread between the sphere and the spring clip. 1 Include values for in your table. T 3 [9] 1(d) (i) Plot a graph of θ on the y-axis against on the x-axis. [3] T 3 (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] (e) It is suggested that the quantities θ and T are related by the equation a θ = + b T 3 where a and b are constants. Use your answers from (d)(iii) to determine the values of a and b. Give appropriate units. a = ...................................................... b = ...................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1 (b) (i) Value for θ in range 40° to 50°, to nearest degree, with unit. [1] (iii) Value for T in range 1.0 to 2.0 s. [1] Evidence of repeat readings. [1] (c) Six sets of values for θ and time (with correct trend) [4] scores 4 marks, five sets scores 3 marks etc. Range: [1] θ values must include 35° or less and 55° or more. Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. 1 / T 3 / s–3, θ (°) or θ (deg) etc. Consistency: [1] All values of T (or nT ) must be given to the nearest 0.1 s, or all to the nearest 0.01 s. Significant figures: [1] Every value of 1 / T 3 must be given to the same number of significant figures as (or one greater than) the significant figures in the corresponding raw time. Calculation: [1] Values of 1 / T 3 calculated correctly. (d) (i) Axes: [1] Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity which is being plotted. Scale markings should be no more than 3 large squares apart. Plotting of points: [1] All observations must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no blobs). Plots must be accurate to within half a small square in both x and y directions. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be no more than ± 5° from a straight line in the y (θ ) direction. (ii) Line of best fit: [1] Judged by balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. Lines must not be kinked or thicker than half a small square. (iii) Gradient: [1] The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with read-off accurate to half a small square in both x and y directions. Or Intercept read directly from the graph, with read-off at x = zero accurate to half a small square in y direction. (e) Value of a equal to candidate’s gradient. Value of b equal to candidate’s intercept. [1] The values must not be fractions. Unit for a is correct and consistent with value. [1] Unit for b is correct and consistent with value. [Maximum mark: 20]

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2 In this experiment you will investigate the motion of a sphere launched from a ramp. (a) Set up the apparatus as shown in Fig. 2.1. Adjust the height of the clamp so that the launch angle φ is approximately 15°. stand clamp mark ramp tray sand wooden block q bench Fig. 2.1 (not to scale) (b) (i) Measure and record φ, as shown in Fig. 2.1. φ = ..................................................[1] (ii) Measure and record the height h1 of the mark above the bench, as shown in Fig. 2.2. mark h1 tray sand h2 bench Fig. 2.2 (not to scale) h1 = ........................................... cm [1] (iii) Measure and record the height h2 of the end of the ramp, as shown in Fig. 2.2. h2 = ................................................. cm (iv) Calculate the speed v of the sphere when it leaves the ramp using the expression v = 2g (h1 – h2) where g = 9.81 m s–2. v = ..................................................[1] (c) Justify the number of significant figures you have given for your value of v. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[1] (d) (i) Place the smaller sphere on the ramp at the mark. Release the sphere. (ii) Measure and record the horizontal distance R from the end of the ramp to the landing position of the sphere, as shown in Fig. 2.3. R Fig. 2.3 (not to scale) R = ............................................ cm [2] (e) Estimate the percentage uncertainty in your value of R. percentage uncertainty = ..................................................[1] (f) By lowering the clamp, increase the launch angle φ to approximately 25°. Repeat (b) and (d) using the same sphere. φ = ...................................................... h1 = ................................................. cm h2 = ................................................. cm v = ...................................................... R = ................................................. cm [3]

Mark scheme: 2 (b) (i) φ in range 10 to 20°, with unit. [1] (ii) Value for h1 to nearest mm. [1] (iv) Correct calculation of v, with correct unit. [1] (c) Justification based on number of significant figures in h1 and h2. [1] (d) (ii) Value of R to nearest mm. [1] Evidence of repeat readings of R. [1] (e) Absolute uncertainty in R in range 2 to 10 mm. [1] If repeated readings have been taken, then the absolute uncertainty can be half the range if the working is shown (but not zero if values are equal). Correct method of calculation to obtain percentage uncertainty. (f) Second values of φ, h1 and h2. [1] Second value of R. [1] Quality: [1] Second R less than first R. (g) (i) Two values of k calculated correctly. [1] (ii) Valid comment consistent with the calculated values of k, testing against a criterion. [1] (h) (i) Two readings are not enough to [4 max] draw a valid conclusion Difficult to measure φ / parallax error when measuring φ Difficult to measure R with reason e.g. parallax error / estimating centre of sphere Sphere rolls after landing φ deflects with marble / ramp not steady / ramp flexible / ball rolls off side / block moves Difficult to release marble from same position each time / difficult to release marble without a force (ii) Take more readings and plot a graph / [4 max] calculate more k values and compare Workable alternative method for φ e.g. measure φ on photo or shadow / larger protractor / draw tangent on block / hold ruler as tangent Use two setsquares to measure R (with description of method) / measure to edge of sphere and add half diameter Video with scale / dye on ball to mark paper / clay to show landing mark / sticky surface to stop rolling Detail of method to make ramp rigid / match sizes of ball and track so that ball runs straight / method of fixing block Use a stop on the ramp / use electromagnetic release [Maximum mark: 20]

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